Yum-Tong Siu (Harvard)

Multiplier ideal sheaves – an interface between analysis and algebraic geometry

Multiplier ideal sheaves identify the location and the extent of failure of estimates in partial differential equations and describe the degeneracy from instability in geometric analysis. They have been applied to such algebraic geometric problems as the Fujita conjecture, the deformational invariance of plurigenera, and the analytic proof of the finite generation of the canonical ring. They have also opened up a new avenue of applying algebraic geometric methods to solvability and regularity problems of partial differential equations. The lecture will start out by introducing multiplier ideal sheaves from original historic perspectives. Then it will focus on the explanation of two techniques. The first is the termination of the Kohn algorithm for subelliptic multipliers. The second is the termination of blow-ups in the analytic proof of the finite generation of the canonical ring.